Circle packing coordinates for the moduli space of tori
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Abstract:
We develop a set of natural coordinates $(\alpha ,\beta )$ on the moduli space of Euclidean tori using the combinatorial structure of circle packings. Surfaces with rational coordinates support Brooks packings, while surfaces with rational $\alpha$ and irrational $\beta$ coordinates support generalized Brooks packings with periodic singularities.References
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Additional Information
- G. Brock Williams
- Affiliation: Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
- Email: brock.williams@ttu.edu
- Received by editor(s): January 18, 2010
- Received by editor(s) in revised form: July 3, 2010
- Published electronically: December 17, 2010
- Communicated by: Mario Bonk
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2577-2585
- MSC (2010): Primary 52C26, 30F60
- DOI: https://doi.org/10.1090/S0002-9939-2010-10690-1
- MathSciNet review: 2784827